Solve systems of linear equations by substitution

Warm-up

Three quick questions from earlier lessons.

Discover

$y = 2x$ and $x + y = 9$ . Since $y$ is $2x$ , you can replace it. What is $x$ ?

Key idea

Substitution turns two equations into one.

A solution of a system makes both equations true: it is where the lines cross. Substitution: solve one equation for a variable, put that expression into the other equation, solve, then substitute back to get the other variable.

Worked example

$y = 3x - 1$ and $2x + y = 14$ .

2x + 3x - 1 = 14

Replace y.

x = 3

5x = 15.

y = 8

Back into y = 3x − 1.

Your turn, guided

Your turn: $y = x + 4$ and $x + y = 10$ . Find $x$ .

x = 3

2x + 4 = 10.

Practice ★

Solve the system $y = 2x + 4$ and $3x + y = 24$ . $x = \;?$
Solve the system $y = 5x + 5$ and $3x + y = 37$ . $x = \;?$

Solve the system $y = 2x + 4$ and $2x + y = 24$ . $y = \;?$

Watch out!

Practice ★★

Solve the system $x = 3y$ and $x + y = 24$ . $y = \;?$
Solve the system $x = 5y$ and $x + y = 24$ . $y = \;?$

Exit ticket

Three questions to check you have got it.

Solve the system $y = 2x + 4$ and $3x + y = 24$ . $x = \;?$
Solve the system $y = 5x + 5$ and $3x + y = 37$ . $x = \;?$
Solve the system $y = 5x + 7$ and $3x + y = 39$ . $x = \;?$

Summary card

Substitution

Replace one variable by its expression, solve, then substitute back.

Watch out: answer the variable the question asks for.

End of the lesson

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